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Using the Euclidean metric, is the set (0, 1) in R^2 open, closed, both, or neither?

  • Thread starter jdinatale
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  • #1
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I typed the question and my attempt at a solution below...

euclidmetric.png


It seems obviously open to me, but I'm not sure how to state it using open balls considering that it's in R^2.
 

Answers and Replies

  • #2
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I typed the question and my attempt at a solution below...

euclidmetric.png


It seems obviously open to me, but I'm not sure how to state it using open balls considering that it's in R^2.
If it's open, its complement is closed. What happens if you sneak up to it from above? Or below?
 

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